Cambridge Primary Mathematics: Teacher's Resource Book with CD-ROM Stage 1

CAMBRIDGE PRIMARY

Mathematics Teacher’s Resource

Cherri Moseley and Janet Rees

Terms and conditions of use University Printing House, Cambridge cb2 8bs, United Kingdom Cambridge University Press is part of the University of Cambridge.

It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107656833 © Cambridge University Press 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

First published 2014 Reprinted 2014 Printed in Poland by Opolgraf A catalogue record for this publication is available from the British Library isbn 978-1-107-65683-3 Paperback Cover artwork: Bill Bolton Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. notice to teachers in the uk It is illegal to reproduce any part of his work in material form (including photocopying and electronic storage) except under the following circumstances: (i) where you are abiding by a licence granted to your school or institution by the Copyright Licensing Agency; (ii) where no such licence exists, or where you wish to exceed the terms of a licence, and you have gained the written permission of Cambridge University Press; (iii) where you are allowed to reproduce without permission under the provisions of Chapter 3 of the Copyright, Designs and Patents Act 1988, which covers, for example, the reproduction for the purposes of setting examination questions. notice to teachers The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for classroom use within the school or institution that purchased the publication. Worksheets and copies of them remain in the copyright of Cambridge University Press, and such copies may not be distributed or used in any way outside the purchasing institution.

This is End User License Agreement (‘EULA’) is a legal agreement between ‘You’ (which means the individual customer) and Cambridge University Press (‘the Licensor’) for Cambridge Primary Mathematics Games Book Stage 1 (‘the Product’). Please read this EULA carefully. By continuing to use the Product, You agree to the terms of this EULA. If You do not agree to this EULA, please do not use this Product and promptly return it to the place where you obtained it.

1. Licence The Licensor grants You the right to use the Product under the terms of this EULA as follows: (a) You may only install one copy of this Product (i) on a single computer or secure network server for use by one or more people at different times, or (ii) on one or more computers for use by a single person (provided the Product is only used on one computer at one time and is only used by that single person). (b) You may only use the Product for non-profit, educational purposes. (c) You shall not and shall not permit anyone else to: (i) copy or authorise copying of the Product, (ii) translate the Product, (iii) reverse-engineer, disassemble or decompile the Product, or (iv) transfer, sell, assign or otherwise convey any portion of the Product.

2. Copyright (a) All content provided as part of the Product (including text, images and ancillary material) and all software, code, and metadata related to the Product is the copyright of the Licensor or has been licensed to the Licensor, and is protected by copyright and all other applicable intellectual property laws and international treaties. (b) You may not copy the Product except for making one copy of the Product solely for backup or archival purposes.

You may not alter, remove or destroy any copyright notice or other material placed on or with this Product. (c) You may edit and make changes to any material provided in the Product in editable format (‘Editable Material’) and store copies of the resulting files (‘Edited Files’) for your own non-commercial, educational use, but You may not distribute Editable Materials or Edited Files to any third-party, or remove, alter, or destroy any copyright notices on Editable Materials or Edited Files, or copy any part of any Editable Material or Edited Files into any other file for any purpose whatsoever.

3. Liability and Indemnification (a) The Product is supplied ‘as-is’ with no express guarantee as to its suitability. To the extent permitted by applicable law, the Licensor is not liable for costs of procurement of substitute products, damages or losses of any kind whatsoever resulting from the use of this Product, or errors or faults therein, and in every case the Licensor’s liability shall be limited to the suggested list price or the amount actually paid by You for the Product, whichever is lower. (b) You accept that the Licensor is not responsible for the persistency, accuracy or availability of any URLs of external or third-party internet websites referred to on the Product and does not guarantee that any content on such websites is, or will remain, accurate, appropriate or available. The Licensor shall not be liable for any content made available from any websites and URLs outside the Product or for the data collection or business practices of any third-party internet website or URL referenced by the Product. (c) You agree to indemnify the Licensor and to keep indemnified the Licensor from and against any loss, cost, damage or expense (including without limitation damages paid to a third party and any reasonable legal costs) incurred by the Licensor as a result of your breach of any of the terms of this EULA. 4. Termination Without prejudice to any other rights, the Licensor may terminate this EULA if You fail to comply with any of its terms and conditions. In such event, You must destroy all copies of the Product in your possession.

5. Governing law This agreement is governed by the laws of England and Wales, without regard to its conflict of laws provision, and each party irrevocably submits to the exclusive jurisdiction of the English courts. The parties disclaim the application of the United Nations Convention on the International Sale of Goods.

Contents The ethos of the Cambridge Primary Maths project Introduction Teaching approaches Talking mathematics Resources, including games Ten Frame

v vii x x x xi

Term 1 1A: Number and problem solving 1 Counting to ten 1.1 Recognising and saying numbers up to ten 1.2 Counting to ten 2 Playing with ten 2.1 Make ten 2.2 Ten take away 2.3 Doubles

1 2 6 11 12 16 18

1C: Measure and problem solving 3 Length 3.1 Measuring length

21 22

1A: Number and problem solving 4 Counting over ten 4.1 Number pairs less than ten 4.2 Ten and some more 5 Estimating 5.1 Estimating 5.2 More estimating

25 26 30 39 40 44

1B: Geometry and problem solving 6 2D and 3D shapes and patterns 6.1 Identifying and sorting 2D shapes 6.2 3D solids 6.3 Symmetry and patterns

47 48 52 56

1A: Number and problem solving 7 Counting beyond 20 7.1 Number pairs to 10 7.2 Beyond 20

59 60 64

1C: Measure and problem solving 8 Capacity (1) 8.1 Measuring capacity 8.2 Estimating capacity 9 Money and time 9.1 Welcome to the class cafĂŠ 9.2 Money 9.3 Telling the time (1) 9.4 Telling the time (2) 10 Comparing weight 10.1 Direct comparison 10.2 Using a bucket balance

69 70 72 75 76 78 80 84 91 92 96

Term 2 2A: Number and problem solving 11 Odd and even numbers 11.1 Pairs – even numbers 11.2 Odd numbers 12 Ordering numbers (1) 12.1 Numbers in order 12.2 Between 13 Combine and take away 13.1 Ten number pairs plus ‌ 13.2 Addition as combining 13.3 Subtraction as take away 13.4 Number line(1) finding the difference 13.5 Number line(2) adding and subtracting two

101 102 106 109 110 114 119 120 122 124 128 130

iii

14 Ordering numbers (2) 14.1 Ordering numbers 14.2 Combinations

133 134 136

2C: Measure and problem solving 15 Money 15.1 What is money?

15.2 A class shop 16 Ordering length and weight 16.1 Length (1) 16.2 Ordering weight 17 Measuring and estimating capacity (2) 17.1 Capacity 17.2 Non-standard measures of capacity 18 Minutes, days and months 18.1 Minutes 18.2 Days of the week 18.3 Months of the year (1)

139 140 144 147 148 150 155 156 160 163 164 168 172

2B: Handling data and problem solving 19 Organising, categorising and representing data (1) 19.1 Sorting into groups 19.2 Pictograms and block graphs 19.3 Venn diagrams

175 176 178 182

Term 3 3A: Number and problem solving 20 Number and the number system: counting in tens 20.1 Counting in tens 20.2 Ten more and ten less 20.3 Tens and ones 21 Number lines, counting on and counting back 21.1 Addition on a number line 21.2 Adding by counting on 21.3 Subtraction by counting back 21.4 Equality

iv

Contents

185 186 188 192 197 198 200 202 206

22 Doubles and halves 22.1 Doubles and near doubles 22.2 Halves of numbers 22.3 Halves of shapes 22.4 Sharing 23 Addition and subtraction: number patterns 23.1 Near tens 23.2 Check subtraction 23.3 What's missing?

211 212 216 218 220 223 224 226 228

3C: Measure and problem solving 24 Money 24.1 How much is money worth?

24.2 Enough money?

25 Comparing length and weight 25.1 Comparing lengths 25.2 Comparison and ordering 26 Further estimating and comparing of capacity 26.1 Measuring capacity 26.2 Solving capacity problems 27 Telling the time and months of the year 27.1 Telling the time (3) 27.2 Telling the time (4) 27.3 Months of the year (2)

231 232 234 237 238 244 247 248 250 253 254 256 258

3B: Handling data and problem solving 28 Organising, categorising and respresenting data (2) 28.1 Collecting and presenting data 22.2 Carroll diagrams 28.3 Sorting data

261 262 266 270

The Ethos of the Cambridge Primary Maths project Cambridge Primary Maths is an innovative combination of curriculum and resources designed to support teachers and learners to succeed in primary mathematics through bestpractice international maths teaching and a problem-solving approach.

To get involved visit www.cie.org.uk/cambridgeprimarymaths 2 1

Cambridge Primary Maths brings together the world-class Cambridge Primary mathematics curriculum from Cambridge International Examinations, high-quality publishing from Cambridge University Press and expertise in engaging online enrichment materials for the mathematics curriculum from NRICH. Cambridge Primary Maths offers teachers an online tool that maps resources and links to materials offered through the primary mathematics curriculum, NRICH and Cambridge Primary Mathematics textbooks and e-books. These resources include engaging online activities, best-practice guidance and examples of Cambridge Primary Maths in action.

The Cambridge curriculum is dedicated to helping schools develop learners who are confident, responsible, reflective, innovative and engaged. It is designed to give learners the skills to problem solve effectively, apply mathematical knowledge and develop a holistic understanding of the subject.

The Cambridge University Press series of Teacher's resources printed books and CD-ROMs provide best-in-class support for this problem-solving approach, based on pedagogical practice found in successful schools across the world. The engaging NRICH online resources help develop mathematical thinking and problem-solving skills.

The benefits of being part of Cambridge Primary Maths are: • the opportunity to explore a maths curriculum founded on the values of the University of Cambridge and best practice in schools • access to an innovative package of online and print resources that can help bring the Cambridge Primary mathematics curriculum to life in the classroom.

3

4

5

1 You can explore the available resources on the Cambridge Primary Maths website by curriculum framework, scheme of work, or teacher resources. In this example, the 'Teacher resources' tab has been selected.

2 The drop-down menu allows selection of resources by Stage.

3 Following selection of the 'Teacher resource' and 'Stage 1', the chapters in the Cambridge University Press textbook 'Teacher's resource 1' are listed.

4 Clicking on a chapter ('2 Playing with 10' in this example) reveals the list of curriculum framework objectives covered in that chapter. Clicking on a given objective (1Nc1 in this example) highlights the most relevant NRICH activity for that objective.

5 A list of relevant NRICH activities for the selected chapter are revealed.

Clicking on a given NRICH activity will highlight the objectives that it covers. You can launch the NRICH activity from here.

v

The Cambridge Primary Maths project provides a complete support package for teachers. The Teacher's Resource is a standalone teaching textbook that can be used independently or together with Cambridge Primary Maths website. The free to access website maps the activities and games in the Teacher's Resource to the Cambridge Primary curriculum. It also highlights relevant online activities designed by the NRICH project team based at the University of Cambridge.

The additional material that the Cambridge Primary Maths project provides can be accessed in the following ways: As a Cambridge Centre: If you are a registered Cambridge Centre, you get free access to all the available material by logging in using your existing Cambridge International Examinations log in details.

Register as a visitor: If you are not a registered Cambridge Centre you can register to the site as a visitor, where you will be free to download a limited set of resources and online activities that can be searched by topic and learning objective.

As an unregistered visitor: You are given free access an introductory video and some sample resources, and are able to read all about the scheme.

vi

Introduction The Cambridge Primary Maths series of resources covers the entire content of the Cambridge Primary mathematics curriculum framework from Cambridge International Examinations. The resources have been written based on a suggested teaching year of three, ten week terms. This can be amended to suit the number of weeks available in your school year.

The Cambridge primary mathematics framework provides a comprehensive set of learning objectives for mathematics. These objectives deal with what learners should know and be able to do. The framework is presented in five strands: the four content strands of Number (including mental strategies), Geometry, Measures and Handling Data are all underpinned by the fifth strand, Problem Solving. Problem solving is integrated throughout the four content strands. Whilst it is important to be able to identify the progression of objectives through the curriculum, it is also essential to bring together the different strands into a logical whole.

This series of printed books and CD-ROMs published by Cambridge University Press is arranged to ensure that the curriculum is covered whilst allowing teachers flexibility in approach. The Scheme of Work for Stage 1 has been fully covered but not in the same order provided by Cambridge International Examinations. You can see from the Contents pages that the authors have moved between, and often returned to, units according to an alternative sequence; the chronological order of units provided in the Scheme of Work has not been adhered to, but the unit numbers and titles have been kept for clarity.

The components of the printed series are as follows: • Teacher’s Resource (printed book and CD-ROM) This resource covers all the objectives of the Cambridge framework through lessons referred to as ‘Core activities’. As a ‘lesson’ is a subjective term (taking more or less time depending on the school and the learners) we prefer to use the terms ‘Core activity’ and ‘session’ to reinforce that there is some flexibility. Each Core activity contains the instructions for you to lead the activity and cover the objectives, as well as providing

expected outcomes, suggested dialogue for discussion, and likely areas of misconception. A section called ‘More activities’ provides you with suggestions for supplementary or extension activities.

The Teacher’s Resource can be used on its own to completely cover the course. (The Learner’s Book and Games Book should not be used without the associated teacher resource, as they are not sufficient on their own to cover all the objectives.)

The accompanying CD-ROM contains: a Word version of the entire printed book. This has been supplied so that you can copy and paste relevant chunks of the text into your own lesson plans if you do not want to use our book directly. You will be able to edit and print the Word files as required but different versions of Word used on different PCs and MACs will render the content slightly differently so you might have some formatting issues.

Questioning – This document outlines some of the different types of question techniques for mathematics and how best to use them, providing support for teachers.

Letters for parents – a template letter is supplied along with a mapping grid to help you to write a letter per Unit of material in order to inform parents what work their child is doing, and what they can do to support their child at home.

Photocopy masters – resources are supplied as PDFs, and as Word files so that you can edit them as required.

• Learner’s Book (printed book) This resource is supplementary to the course. As the ethos of the Cambridge Maths Project is to avoid rote learning and drill practice, there are no accompanying workbooks. The Learner’s Book instead combines consolidation and support for the learner with investigations that allow freedom of thought, and questions that encourage the learner to apply their knowledge rather than just remembering a technique. The investigations and questions are written to assess the

vii

learner’s understanding of the learning outcomes of the Core activity.

Learners can write down their answers to investigations and questions in an exercise book in order to inform assessment. The overall approach of the Teacher’s Resource accompanied by the Learner’s Book allows a simple way for you to assess how well a learner understands a topic, whilst also encouraging discussion, problem-solving and investigation skills.

At Stage 1, the Learner’s Book acts as a useful support tool for the learners by providing visual reminders or points for discussion to develop problem-solving skills and support learning through discovery and discussion. Ideally, a session should be taught using the appropriate Core activity in the Teacher’s Resource 1, with the Learner’s Book open at the correct page in order to provide visual reminders and support; additional investigations beyond the Core activity are not provided in the Learner’s Book at this Stage on the basis that learners are too young for independent study.

There is generally a single page in the Learner’s Book for each associated Core activity in the Teacher’s Resource for Stage 1. The Teacher’s Resource will refer to the Learner’s Book page by title and page number, and the title of the Core activity will be at the bottom of the Learner’s Book page. Please note that the Learner’s Book does not cover all of the Cambridge objectives on its own; it is for supplementary use only.

• Games Book (printed book and CD-ROM) This resource is complete in its own right as a source of engaging, informative maths games. It is also a supplementary resource to the series. It can be used alongside the Teacher’s Resource as a source of additional activities to support learners that need extra reinforcement, or to give to advanced learners as extension. Each game comes with a ‘Maths focus’ to highlight the intended learning/reinforcement outcome of the game, so that the book can be used independently of any other resource. For those who are using it as part of this series, relevant games are referred to by title and page number in the ‘More activities’

viii

Introduction

section of the Teacher’s Resource. The accompanying CD-ROM contains nets to make required resources; it also contains a mapping document that maps the games to the other resources in the series for those who require it. Please note that the Games Book does not cover all of the Cambridge objectives on its own; it is for supplementary use only.

Each chapter in the Teacher’s resource includes • A Quick reference section to list the title of each of the Core activities contained within the chapter. It provides an outline of the learning outcome(s) of each Core activity. (See page vii and later in this list, for a reminder of what is meant by a Core activity.)

• A list of the Objectives from the Cambridge primary mathematics curriculum framework that are covered across the chapter as a whole.

Please note that this means that not all of the listed objectives will be covered in each of the chapter’s Core activities; they are covered when the chapter is taken as a whole. The objectives are referenced using subheadings from the framework, for example ‘1A: Calculation (Mental strategies)’ and the code from the Scheme of Work, for example, ‘2Nc3’.

Please be aware that the content of an objective is often split across different Core activities and/or different chapters for a logical progression of learning and development. Please be assured that provided you eventually cover all of the Core activities across the whole Teacher’s Resource, you will have covered all of the objectives in full.

It should be clear from the nature of a Core activity when parts of an objective have not been fully covered. For example, a chapter on length will list ‘Measure’ objectives that also include weight, such as ‘1MI1’ (Compare lengths and weights by direct comparison…) but the weight aspect of the objective will not be covered in a chapter on length(!); that part of the objective will be covered in a chapter on weight. Or a chapter focussing on understanding teen numbers as ‘ten and some more’ might cover the action ‘recite numbers in order’ but only up to 20 and therefore only partially cover objective ‘1Nn1’ (Recite numbers in

order … from 1 to 100…)). But please be reassured that, by the end of the Teacher’s resource, all of objectives 1MI1 and 1Nn1 will have been covered in full; as will all objectives. The Summary bulleted list at the end of each Core activity lists the learning outcome of the activity and can add some clarity of coverage, if required.

• A list of key Prior learning topics is provided to ensure learners are ready to move on to the chapter, and to remind teachers of the need to build on previous learning.

• Important and/or new Vocabulary for the chapter as a whole is listed.

Within the Core activity itself, relevant vocabulary will be repeated along with a helpful description to support teaching of new words.

The Core activities (within each chapter) collectively provide a comprehensive teaching programme for the whole stage. Each Core activity includes: • A list of required Resources to carry out the activity. This list includes resources provided as photocopy masters within the Teacher’s Resource printed book (indicated by ‘(pxx)’), and photocopy masters provided on the CD-ROM (indicated by ‘(CD-ROM)’), as well as resources found in the classroom or at home. ‘(Optional)’ resources are those that are required for the activities listed in the ‘More activities’ section and thus are optional.

• A main narrative that is split into two columns. The left-hand (wider) column provides instructions for how to deliver the activity, suggestions for dialogue to instigate discussions, possible responses and outcomes, as well as general support for teaching the objective. Differences in formatting in this section identify different types of interactivity: Teacher-led whole class activity The main narrative represents work to be done as a whole class.

Teacher-Learner discussion “Text that is set in italics within double-quotation marks represents suggested teacher dialogue to instigate Teacher-Learner disccusion.”

Learner-Learner interaction

The right-hand (narrow) column provides, the vocabulary panel side-notes and examples a Look out for! panel that offers practical suggestions for identifying and addressing common difficulties and misconceptions, as well as how to spot advanced learners and ideas for extension tasks to give them an Opportunity for display panel to provide ideas for displays.

• A Summary at the end of each Core activity to list the learning outcomes/expectations following the activity. This is accompanied by a Check up! section that provides quick-fire probing questions useful for formative assessment; and a Notes on the Learner’s Book section that references the title and page number of the associated Learner’s Book page, as well as a brief summary of what the page involves.

• A More activities section that provides suggestions for further activities; these are not required to cover the objectives and therefore are optional activities that can be used for reinforcement and differentiation. The additional activities might include a reference to a game in the Games Book. You are encouraged to also look on the Cambridge Maths Project website to find NRICH activities linked to the Cambridge objectives. Together, these activities provide a wealth of material from which teachers can select those most appropriate to their circumstances both in class and for use of homework if this is set.

We would recommend that you work through the chapters in the order they appear in this book as you might find that later chapters build on knowledge from earlier in the book. If possible, work with colleagues and share ideas and over time you will feel confident in modifying and adapting your plans.

Group and pair work between learners is encouraged throughout and is indicated using a grey panel behind the text and a change in font.

Introduction

ix

Teaching approaches Learners have different learning styles and teachers need to appeal to all these styles. You will find references to group work, working in pairs and working individually within these materials.

The grouping depends on the activity and the point reached within a series of sessions. It may be appropriate to teach the whole class, for example, at the beginning of a series of sessions when explaining, demonstrating or asking questions. After this initial stage, learners often benefit from opportunities to discuss and explain their thoughts to a partner or in a group. Such activities where learners are working collaboratively are highlighted in the main narrative as detailed in the previous section.

High quality teaching is oral, interactive and lively and is a two-way process between teacher and learners. Learners play an active part by asking and answering questions, contributing to discussions and explaining and demonstrating their methods to the rest of the class or group. Teachers need to listen and use learner ideas to show that these are valued. Learners will make errors if they take risks but these are an important part of the learning process.

Talking mathematics We need to encourage learners to speak during a maths session in order to: • communicate • explain and try out ideas • develop correct use of mathematical vocabulary • develop mathematical thinking.

x

Introduction

It is important that learners develop mathematical language and communication in order to (using Bloom’s taxonomy): Explain mathematical thinking (I think that . . . because . . .)

Develop understanding (I understand that . . .)

Solve problems (I know that . . . so . . .)

Explain solutions (This is how I found out that . . .)

Ask and answer questions (What, why, how, when, if . . .)

Justify answers (I think this because . . .)

There is advice on the CD-ROM about the types of questioning you can use to get your students talking maths (Questioning).

Resources, including games Resources can support, assist and extend learning. The use of resources such as Ten frames, 100 squares, number lines, digit cards and arrow cards is promoted in the Teacher’s Resource. Games provide a useful way of reinforcing skills and practising and consolidating ideas. Learners gain confidence and are able to explore and discuss mathematical ideas whilst developing their mathematical language.

Calculators should be used to help learners understand numbers and the number system including place value and properties of numbers. However, the calculator is not promoted as a calculation tool before Stage 5.

NRICH have created an abundance of engaging and well-thought-out mathematical resources, which have been mapped to the Cambridge Primary scheme of work, and are available from the Cambridge Primary Maths website. Their interactive and downloadable activities can provide an alternative learning style or enrichment for some of the core concepts.

The Ten Frame To develop understanding of number relationships Once learners are confident that the frame will always hold ten objects, no matter what those objects are, the frame can be used to help develop a learner’s understanding of number relationships.

The Ten Frame is used throughout Stage 1 and into Stage 2 as a simple, consistent image of the number ten. Ten is a key part of our number system and it is essential to help learners develop a clear picture of ten that they can use and manipulate.

The Ten frame can be used in so many ways to illustrate number and is not restricted to numbers to ten. It provides a strong image of ten that helps learners to develop an awareness of the size of numbers, leading to the understanding of place value. Such an understanding is vital for mental calculations and a deep understanding of our number system.

As a counting frame The Ten frame can be introduced as a simple counting frame. Learners count objects onto the frame by placing one in each space, using the ten frame as a mat to work on. Doing this with a variety of objects helps learners to understand that numbers can be transferred from one object to another. This solid grounding is essential. They are not simply counting but are building an image of ten and numbers to ten that will support their understanding of our number system.

Eventually, the Ten frame becomes an image of ten in its own right and learners no longer need to place an object in each space. They can use it to support counting in tens, and can instantly recognise the arrangement of numbers below ten. This recognition means that you can also cut the Ten frame to show each single digit number, supporting learners to develop understanding of place value.

Addition Placing nine objects of one colour and one object of a different colour helps learners to clearly see that nine and one more makes ten. All the number pairs (or additions) to ten can be explored in this way. Learners can be shown the shorthand that we use to write these relationships down (9 + 1 = 10) and they can begin to record what they see.

Subtraction Later, subtraction can be explored in the same way as addition. With ten objects on the Ten frame, removing one but keeping it within sight clearly shows that ten take away one leaves nine (10 – 1 = 9).

Doubles With the Ten frame orientated horizontally across the page or desk, placing a counter of one colour on the bottom row and one of a different colour on the top row allows learners to explore double 1, then double 2, 3, 4 and 5.

Numbers beyond ten As learners begin to extend their understanding from ten to 20, a second Ten frame helps them to see these numbers as ‘ten and some more’, again laying firm foundations for understanding the number system.

Even and odd By consistently using the pattern of twos, odd numbers always have an unmatched space, while even numbers are rectangles.

The Ten Frame

xi

xii

Blank page

1A

1 Counting to ten

Quick reference Important note: chapter 1 is different in nature from the other chapters in this resource. It offers some general ideas for activities you could do to introduce learners to counting whereas the rest of the resource offers more specific activities. Decide whether you need to include the activities of chapter 1 based on the ability of the learners in your class. If they are confident in counting numbers from 1 to 10, you could start at chapter 2.

Core activity 1.1: Recognising and saying numbers up to ten (Learner’s Book p4–5) Learners use number songs, rhymes and stories to say the numbers from one to ten, recognise the associated numerals and understand the meaning of counting.

Numbers

How many?

How many in each group?

Vocabulary count How many?

1, 2, ...

Core activity 1.2: Counting to ten (Learner’s Book p6) Learners accurately count to ten in a wide variety of situations.

4 count How many?

count

1, 2, ...

5

1 2 3 4 5 6 7 8 9 10 4

Unit 1A Core activity 1.1 Recognising and saying numbers up to ten

5

6

Unit 1A Core activity 1.2 Counting to ten

please note that listed objectives might only be partially covered within any given chapter but are covered fully across the book when taken as a whole

Prior learning

Objectives* –

• Learners must have recognition of some spoken words for number.

• Playing at counting.

• Say the numbers one to five in order.

1A: Numbers and the number system 1Nn1 – Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).

1Nn2 – Read and write numerals from 0 to 20.

1Nn3 – Count objects up to 20, recognising conservation of number. *for NRICH activities mapped to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths

Vocabulary one • two • three • four • five • six • seven • eight • nine • ten • amount • number • how many? • count

Cambridge Primary Mathematics 1 © Cambridge University Press 2014

Unit 1A

1

Core activity 1.1: Recognising and saying numbers up to ten

LB: p4–5

Resources: Number stories, rhymes and songs (see Maths rhymes for examples (CD-ROM)). Counting resources such as counters, straws, balls, sticks, beads and cubes. Materials for creating a washing line such as string and clothes pegs. Materials for practising writing numerals such as sand trays, foam, paint, chalk, pens, dough etc. Numeral practice photocopy master (p9). (Optional: Shirts photocopy master (CD-ROM); materials for decorating and/or printing such as scrap paper and card, corks, buttons, bottle tops, and paint; large paper or card; empty plastic drinks bottles and coloured sticky tape/paper.)

Learners need to become fluent at counting to five initially, then to ten. At first, learners might simply copy the sounds, so meaning needs to be added through lots of practical counting activities.

To say the numbers from one to ten correctly in the right order, learners need plenty of experience of hearing and saying the numbers. Read number stories, and sing or say number rhymes modelling actions for the learners to copy. Learners often have favourite number songs from their local culture that they request to hear and sing again and again. This repetition helps them to remember the numbers used and what they represent.

Opportunity for display Depending on the age ranges in your class, create an ‘Age display’. Display colourful numerals and pictures of the children around a sentence such as ‘We are 4!’; ‘We are 5!’ and/or ‘We are 6!’ You could make a border from birthday cards contributed by the learners after their special day. When a learner has a birthday, make sure they move from one display to another.

Use a range of counting resources such as counters, straws, balls, sticks, beads and cubes.

There should be many counting rhymes and songs from the local culture, use these if the learners are familiar with them from pre-school clubs or you can use your own selection or there are some ideas on the Maths Rhymes photocopy master. Useful early ones often include finger actions, for example, One, two, three, four, five, once I caught a fish alive.

Many rhymes count backwards. Ensure that counting forwards is secure before attempting to count backwards. Check learners are ready to count backwards by doing the counting that the rhyme demands as a class first, before singing or saying a rhyme that counts backwards. (For example, in the rhyme Five little ducks went swimming one day count the five little ducks. Or in the rhyme Five currant buns in a Baker’s shop count the five currant buns. (These rhymes have not been supplied but should be easy to find online.). If you have pictures of the items you sing about, peg these on a washing line and give learners the opportunity to peg them in order themselves, and to add or remove them as the song is sung.

2

Unit 1A

1 Counting to ten

Example: pegging on a washing line.

Model counting behaviour as you share the song/rhyme, sometimes using counting resources and sometimes using the learners themselves. If the numeral in the story is written on the page, then draw attention to it. As the learners become familiar with the shape of the numeral practise writing it in the air. Learners will copy your actions, so make sure that you write the numeral in the air back to front so that they see it the right way round and learn the shape correctly.

Move on to writing numerals in wet and dry sand, then writing them using foam, paint, chalk and chunky pens, and/or modelling them in dough and in many other ways before asking the learners to record on paper. Use the Numeral practice photocopy master when learners are ready to write the numerals. Give learners lots of opportunity to practise forming numerals.

Example: writing the number ‘3’ in the air.

Teacher view Learner view whilst whilst writing. teacher is writing.

3

Look out for!

• Learners who reverse numerals when writing, for example writing 3 more like a capital ‘E’; or learners who get confused between the appearances of two similar-looking numbers, for example 5 and 3 are commonly mistaken for each other by learners. Show them how to write it correctly, or count to identify the correct number.

• Learners who might know some larger numbers, for example the age of a sibling or a door number. Support them to find this number on a number line and to write it if they wish.

Summary Learners are able to recite the numbers one to ten in order and begin to recognise the matching numeral.

Notes on the Learner’s Book Numbers (p4): point to the numerals and say their name in order together. Learners might like to refer back to this page later to remind them of the numbers one to ten.

Up to 10 (p5): count the items and look at the shape of the matching numeral.

Check up!

Sing a familiar song or rhyme together, allowing the learners to take the lead and supporting only when necessary.

Core activity 1.1: Recognising and saying numbers up to ten

3

More activities Shirts (individuals) You will need the Shirts photocopy master (CD-ROM).

Use the Shirts photocopy master to encourage learners to count or sing along the line, and to fill in the missing numbers.

My number (individuals) You will need materials for decorating/printing, such as scrap paper and card, corks, buttons and bottle tops, and paint.

Learners readily recognise and say their age. Learners cut-out large numerals of their age and decorate it. Learners could print on their numeral using corks and other shapes dipped in paint. When a learner has a birthday, make sure they decorate a new number.

Order (groups) You will need paper or card for making large 1 to 10 number cards and resources for making a washing line, such as string and pegs.

Make large number cards, with the number on both sides so learners can always see which number they are holding. Ten learners each hold a number card and move themselves into the correct order (from one to ten) in time with a chosen number song, which is being sung by the rest of the class. Ask each learner to give their card to a friend who doesn’t have one, then repeat the activity using a different song or rhyme. Start with songs and rhymes up to 5 first. These number cards could also be pegged on a washing line as the learners sing a counting song. They can also be removed one at a time when counting back from ten to one.

Number rockets (groups) You will need empty plastic drinks bottles and coloured sticky tape or coloured paper.

Learners put a different number on each differently coloured rocket. Learners line up the rockets in order, with 1 at the far right-hand side of the line.

Learners will enjoy counting back along the line of rockets and shouting ‘blast off’ after saying 1.

4

Unit 1A

1 Counting to ten

Blank page

5

Core activity 1.2: Counting to ten

LB: p6

Resources: (Optional: counting materials such as counters, straws, balls, sticks, beads, cubes, feathers, stones, beans, small bells, pompoms, mini cars, assorted buttons, bottle tops as well as commercial sets; assorted containers for learners to count into, such as small bowls, empty boxes and cartons; Number tracks photocopy master (chapter 4, p38); 0–9 digit cards photocopy master (CD-ROM) for learners to label their counts with; a set of ten containers, each labelled with a different number. Provide equipment such as pens, paper and sticky labels for learners to make their own labels.

Materials for decoration, such as paint, coloured paper, glue, pictures cut from magazines, pens and pencils; sheets of A4 paper and a stapler.)

Learners need lots of experience of counting to understand what a number really means, for example, to understand ‘the threeness of three’. Songs, rhymes and stories help learners to get the words in the right order, but unless they count items one by one and realise that the last number said is the total, learners cannot really count.

Stories often use contexts that the learners enjoy and this helps to give the counting a real purpose. Stories such as Goldilocks and the three bears, The three billy goats Gruff and others provide lots of opportunity to count to three. You might be counting bowls of porridge, bears or goats. This helps the learners to recognise that anything can be counted. Each country will have its own familiar traditional stories. Some counting stories will lead to activities that the learners can carry out to practise counting. If a story uses ten black spots in a large variety of pictures, learners can then make their own pictures with a particular number of coloured spots. Stories which focus on counting legs could be followed up by learners creating their own creature with a particular number of legs. And so on.

Actions and sounds can also be counted. Learners could tap drums, shake tambourines, clap or jump a particular number of times. They also need to count things they cannot touch, such as clouds, or things that are simply out of reach.

Opportunities for counting are all around us and learners will be happy to join in, even if the numbers go beyond the range they understand.

6

Unit 1A

1 Counting to ten

Look out for!

• Learners who frequently miscount and need more practice at touching and moving each object as it is counted. Encourage them to slow down and exaggerate their movements so they can be sure of what has been counted and what still needs to be counted.

• Learners who can confidently count objects up to ten. Challenge them with questions such as, “What if there was one more?”

Summary Learners are able to accurately count to ten in a wide variety of situations.

Notes on the Learner’s Book How many? (p6): ask learners how many shells there are in each group. They could then draw a group of shells for a counting number they know, or for a number that is missing from the Learner’s Book page.

Check up!

• Show the learners a small handful of items and invite them to count them with you.

• Alternatively, begin to count as you clap and encourage learners to join in then take over.

More activities Counting box (individuals, groups or class) You will need counting materials such as counters, straws, balls, sticks, beads, cubes, feathers, stones, beans, small bells, pompoms, mini cars, assorted buttons, bottle tops as well as commercial sets. Assorted containers for learners to count into, such as small bowls, empty boxes and cartons. Number tracks. Number cards for learners to label their counts with. A set of ten containers, each labelled with a different number. Pens, paper and sticky labels for learners to make their own labels.

Create a counting box for the learners to explore when they have completed an activity or during free time. Make the box interesting and enticing by decorating it as a treasure chest or something else that will appeal to the learners. Add sets of counting materials in assorted containers and some number tracks. Make sure the sets are of interest and change them regularly to ensure the learners are curious enough to revisit the box. Provide small bowls, boxes or containers for the learners to count into and number cards for learners to label their counts with. You could also provide a set of ten containers, each labelled with a number. Provide equipment such as pens, paper and sticky labels for learners to make their own labels.

Number street (class) You will need empty boxes and materials for decoration.

Make a street of houses from empty boxes and other materials. Learners can complete the houses according to the house number. So house number one has one window, one door, one of anything the learners would like to include (tree, bush etc.). Arrange the houses into a street.

Opportunity for display Display the houses made for ‘Number street’ along a drawn road. Make matching gardens too. Ask questions such as, “Who might live here? How can you tell which number this house is?”

Core activity 1.1: Recognising and saying numbers up to ten

7

Counting books (individuals or pairs) You will need sheets of A4 paper, a stapler, glue, pictures and drawing materials.

Fold three sheets of paper in half and staple in the middle to form a book. Start with a large number 1 on the inside front cover and continue to number 10 on the inside back cover. You could draw these numerals and photocopy the sheets before stapling together. Learners then draw or stick the matching number of items on each page. Books could be themed: toys, bugs, animals and so on. Place the completed books in the book area for everyone to share.

Alternatively, pair up the learners so that they interview one another to find out their interests, then illustrate the book according to those interests.

When the learners deliver the counting books, make sure there is time for each pair to share the book together. Put the books in your reading area so that everyone can enjoy them.

Games Book (ISBN 9781107646407) Race to school (p1) is a game for up to four players. It reinforces accurate counting of small numbers.

Dice grid (p1) is a game for two players. It helps the learners to match their count and the numeral.

8

Unit 1A

1 Counting to ten

Numeral practice

1 2 3 4 5 Instructions on page 3.

Original Material Š Cambridge University Press, 2014

6 7 8 9 10 Instructions on page 3

Original Material Š Cambridge University Press, 2014

1A

2 Playing with ten

Quick reference Core activity 2.1: Make ten (Learner’s Book p7) Learners use a Ten frame to practise finding number pairs to ten.

Core activity 2.2: Ten take away (Learner’s Book p8) Learners use a Ten frame to practise finding ‘take away’ facts for ten using number pairs to ten.

Make ten Find two numbers to make ten.

Ten take away How many are there left?

Vocabulary

Doubles Double 1 makes 2.

ten frame

Vocabulary double

Double 2 makes 4.

Find three numbers to make ten.

What other doubles can you find?

Core activity 2.3: Doubles (Learner’s Book p9) Learners use a Ten frame to practise finding double 1, 2, 3, 4 and 5.

Prior learning • Count in ones to ten and beyond.

• Read and write numbers to ten and beyond.

Objectives* – 1Nn1 – 1Nn2 – 1Nn3 – 1Nc1 – 1Nc5 – 1Nc8 – 1Nc9 – 1Nc11 –

Unit 1A Core activity 2.1 Make ten

7

8

Unit 1A Core activity 2.2 Ten take away

Unit 1A Core activity 2.3 Doubles

9

please note that listed objectives might only be partially covered within any given chapter but are covered fully across the book when taken as a whole

1A: Numbers and the number system Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).

Read and write numerals from 0 to 20.

Count objects up to 20, recognising conservation of number.

1A: Calculation (mental strategies) Know all number pairs to 10 and record the related addition/subtraction facts.

Know doubles to at least double 5.

1A: Calculation (Addition and subtraction) Understand addition as counting on and combining two sets; record related addition sentences.

Understand subtraction as counting back and ‘take away’; record related subtraction sentences.

Add/subtract a single-digit number by counting on/back.

*for NRICH activities mapped to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths

Vocabulary Ten frame • number pair (or bond) • add • equals • take away • double

Cambridge Primary Mathematics 1 © Cambridge University Press 2014

Unit 1A

11

Core activity 2.1: Make ten

LB: p7

Resources: Packaging that contained ten items (e.g. biscuits, pencils, egg carton). Ten frame photocopy master (p20). Resources for counting: counters, cubes or other counting objects in two different colours. 0–9 digit cards photocopy master (CD-ROM). (Optional: a set of ten objects and a container that will hold the ten objects. A set of ten pictures or the Monsters hunt photocopy master (CD-ROM). A hole punch or scissors and string. Mystery number pair to 10 photocopy master (CD-ROM).)

Count with the learners how many fingers they have. Explain that ten is a very important number in our number system. We count in tens and use ten all the time, perhaps because we have ten fingers. You could show the learners some food or other packaging which contained ten items, to show that lots of things come in tens.

number pair to ten: two numbers that add together to make ten, for example, 7 + 3 = 10.

Finding number pairs to ten

equals: has the same amount or value as; the sign is =.

Explain that because ten is a very useful number, we need to get to know it really well. Give each learner one Ten frame from the Ten frame photocopy master. Count the squares with them. Give the learners ten counters (or cubes or other counting objects) in one colour and ten in another colour. Ask them to put a counter of the same colour on each square of their ten frame.

Look out for!

“How many counters do you need of the other colour to fill the Ten frame?” The learners will tell you that there is no more room to add other counters. Tell them, “You are right: ten and 0 makes ten.” Swap one counter at the right-hand end for the other colour. “Now how many are there of the first colour?” (Answer: nine) “How many of the second colour?”

(Answer: one). Say the number sentence, “Nine and one makes ten.” Continue in this way until all the counters have been swapped for the second colour. You could ask learners to record the number pairs on a sheet of Ten frames by colouring in the squares, or by recording the number sentences. For example:10 and 0 makes 10; 10 + 0 makes 10; 10 + 0 = 10 or in some other way. Explain that our number pairs for ten are an example of combining two sets of objects together and this is known as addition. Repeat the number sentence, this time using ‘add’ or ‘plus’. For example, ‘7 plus 3 is 10’.

12

Vocabulary

Unit 1A

2 Playing with ten

• Learners who make mistakes when counting the counters. Check that they are pointing to each counter and not missing one out or counting one twice. Provide further opportunities to practise counting.

• Learners who can predict the second number to make ten or recognise a pattern. Challenge them to find all the number pairs for another number.

Call out a number less than 10 and ask the learners to count on to 10. Explain that counting on from a starting number to a target number is another way of adding. Repeat this activity for other numbers less than 10 so that the learners gain confidence in counting on. Then extend the activity by calling out a number and asking them to call out the corresponding number pair without counting on. They can always return to using their Ten frames and counters for the number pairs that they struggle to remember. Make use of the fact that we have ten fingers by practising quick additions to ten using fingers.

Opportunity for display Display a coloured set of ten frames showing all the number pairs to ten with the matching number sentences.

You will need to decide whether to continue the activity by matching the number pairs that are simply reversals, for example 3 and 7 or 7 and 3, or whether this is better left until the learners are more confident.

Summary Learners have begun to know the number pairs to ten and have learnt useful strategies to find out the number pairs that they cannot recall.

Notes on the Learner’s Book Make ten (p7): learners use the Ten frame and counters of two different colours to practise finding two numbers to make ten. They could then explore using three numbers to make ten, using counters of three different colours.

Check up!

“Here is a set of number cards from zero to ten.”

• “Make ten with two cards.”

• “Which card do you have left over?”

• “You need more cards to make all the number pairs for 10. Which numbers do you need (5 and 10)?”

“I have three blue counters. How many green ones do I need to make ten altogether?”

More activities Peek-a-boo (class) You will need the Ten frame photocopy master, a set of ten objects, a container that will hold the ten objects.

Count a set of ten objects onto a Ten frame with the learners. Tip the objects out into a container, making sure the learners know that there are still ten.

The learners close their eyes and you remove some of the objects, holding them in your fist so learners cannot see them. When learners have opened their eyes they guess or work out how many objects you are holding. Show them how to count what is left onto a ten frame and count the empty spaces to find out how many objects you are holding. Verbalise what the learners found out, for example, “Seven in the pot and three in my hand makes ten altogether.”

Play the same game with different numbers of objects, making sure that learners understand how many you are working with each time.

Core activity 2.1: Make ten

13

Ten memory game (pairs) You will need a set of cards from the 0–9 digit cards photocopy master (CD-ROM), with one additional ‘5’ card.

Shuffle the cards and place them face down in a four by three grid. Learners take it in turns to turn over two cards. If the two cards make ten, they can keep them; if not, they must return them face down in their original positions. The learner who collects the most cards is the winner.

Ten snap (pairs or groups) You will need two sets cards from the 0–9 digit cards photocopy master (CD-ROM) with two additional ‘5’ cards. (Use one set of cards per player.)

Shuffle the two sets of cards. Deal all the cards out to the players, face down. Players take it in turns to turn over their top card and place it in the middle of the table. Players call out ‘Snap’ when two consecutive cards make a number pair to ten.

Monster hunt (class) You will need a set of ten pictures that reflect learners’ interests or the Monster hunt photocopy master (CD-ROM); a hole punch or scissors and string.

Label the ten pictures from 1 to 10. Punch a hole near the top of each picture and tie a loop of string through the hole. Hang up the pictures in various places around the classroom/school and challenge learners to find them all. During the day, frequently check with the learners which pictures have been found and which are still hiding, by ordering the numbers from one to ten. You could extend beyond ten.

Mystery number pair to ten (class) You will need the Mystery number pair to 10 photocopy master (CD-ROM).

Read aloud the clues on the photocopy master to help learners find the mystery number pair to ten.

Games Book (ISBN 9781107646407) Playing with 10(1): Making 10 (p4) is a game for two players. It can be used to help learners recognise the different ways of making ten.

14

Unit 1A

2 Playing with ten

Blank page

15

Core activity 2.2: Ten take away

LB: p8

Resources: Resources for counting: counters, cubes or other counting objects. Ten frame photocopy master (p20). (Optional: 0–9 digit cards photocopy master (CD-ROM). Mystery 10 take away photocopy master (CD-ROM).)

Explain to the learners that this is another activity to help us get to know the number ten better. Count from 0 to 10, forwards and back, as a class.

Finding number pairs for subtraction to ten Give each learner one Ten frame from the Ten frame photocopy master. Count the squares with them. Give each learner ten counters (or cubes or other counting objects) and ask them to place one counter in each square. “Can you see just by looking how many counters you have?”

Ask each learner to take one counter off the Ten frame, from the right-hand end. Explain that we had 10 and we have ‘taken away’ 1. “How many do we have left?”

1

9

You could ask the learners to record this on a sheet of Ten frames by colouring in the squares, or by writing down: 10 → 1 leaves 9; 10 − 1 leaves 9; 10 − 1 = 9, or in some other way.

Tell learners, “Put the counter back where it was on the frame. Now take away two counters.

How many do we have left?” If you wish to record, continue as before: 10 → 2 leaves 8; 10 – 2 leaves 8; 10 – 2 = 8 Continue like this until you have taken away all ten counters. You could also take away zero counters. Explain that ‘take away’ is another term for subtraction. Ask the learners to place 10 counters on their Ten frame again. This time, tell them that we are going to take away 4 by counting back. Start at 10, then as you say ‘9’ remove one counter, then as you say ‘8’ remove another and so on until you have removed 4 counters and in doing so have counted back 4. Explain that this is another way they can subtract a number from 10.

16

Unit 1A

2 Playing with ten

Look out for!

• Learners who make mistakes when counting the counters. Check that they are pointing to each counter and not missing one out or counting one twice. Provide further opportunities to practise counting.

• Learners who can predict the next take away pair because they have recognised a pattern. Challenge them to find all the take away pairs for another number.

Example: using a Ten frame to show 10 – 2 = 8.

8

2

Practise by calling out ten take away [insert a number less than or equal to 10], asking the learners to take away the number you say and tell you how many are left. Show the learners how to use their fingers to help. You may need to revisit or repeat this activity to enable all the learners to feel confident in taking away.

Summary Learners have begun to know the subtraction pairs for ten and have learnt a useful strategy to find out the subtraction pairs that they cannot recall.

Notes on the Learner’s Book Ten take away (p8): learners use the Ten frame to practise finding number pairs for subtraction from ten.

Check up!

“Show me ten fingers.”

• “Fold three fingers away; ten take away three leaves?”

• “What if you folded four fingers away?”

• “How many fingers do you need to fold away to leave six?”

Encourage learners to say the complete number sentence aloud.

More activities Ten take away memory game (pairs) You will need a set of cards from the 0–9 digit cards photocopy master (CD-ROM) with an additional ‘5’ card.

Shuffle the cards and place them face down in a 4 by 3 grid. Learners take turns to turn over two cards. If the two cards make ten, they can keep them; if not, they must return them face down in their original positions. The learner who collects the most cards is the winner. When the learners find pairs of cards to make ten, they must say the corresponding number sentence in order to keep the cards. For example, ‘10 take away 3 leaves 7’ or ‘10 take away 7 leaves 3’ to keep the cards.

Mystery ten take away (class) You will need the Mystery 10 take away photocopy master (CD-ROM).

Read aloud the clues on the photocopy master to help learners find the mystery take away number pair to ten.

Games Book (ISBN 9781107646407) Playing with 10(2): Take away from 10 (p4) is a game for two players. It will help learners to recognise the different ways of making ten.

Core activity 2.2: Ten take away

17

Core activity 2.3: Doubles

LB: p9

Resources: Ten frame photocopy master (p20). A piece of string or a stick to place across the ten frame. Ten cubes: five of one colour, five of another colour. (Optional: 0–9 digit cards photocopy master (CD-ROM). Different coloured dice and cubes. Dominoes (CD-ROM).)

Remind learners that they have been finding out all about ten. Say, “There was one number that we needed two of to make ten. What was that number?” Learners should be able to tell you that this was five.

Show learners a Ten frame and place a piece of string or a stick, horizontally across the middle. Put five cubes of the same colour along the top row and five of a different colour along the bottom row. Remind learners of the number sentence, “five and five makes ten”. Now stack the five cubes from the top row and then the five cubes from the second row separately, away from the Ten frame and say, “Double five makes ten. What do you think ‘double’ means?”

Draw at that it means ‘two lots of, the same amount twice and multiply by 2’.

You could talk about how sometimes people say they are ‘seeing double’, meaning they saw two of something. People might also say that they have a ‘double’, someone who looks exactly the same as they do, like an identical twin.

Ask the learners if they think there is another number they could double to make ten. From their experience with the first two core activities, they should be able to say that only five will work.

Continue to work in the same way to find double 1, 2, 3 and 4. You could also extend this to finding doubles to ten using two Ten frames.

Look out for!

• Learners who are not sure what ‘double’ means.

Make a tower of between two and five cubes and ask the learner to make another that is the same as yours. Explain, “Now we have double the number of cubes because we have two lots that are the same.” Count the cubes in both towers and say, for example, “Double three is six.”

• Learners who are comfortable working with higher numbers. Challenge them to find out doubles to double ten.

Opportunity for display Display several towers made from cubes with a sign inviting learners to find doubles, and label them.

Summary Learners understand what double means and are able to find doubles of the numbers one to five.

Notes on the Learner’s Book Doubles (p9): learners can use the Ten frame to practise finding doubles, up to double five.

18

Unit 1A

2 Playing with ten

Check up!

“How many cubes will you need to make two towers that each have three cubes?” (Answer: six) Learners say their answer and then make the towers to see if they were right. Repeat for other numbers from one to five.

More activities Finger doubles (class) Use the fingers on each hand to make doubles. For double 1, show a finger on each hand and bring them together saying, “Double one is two”. Continue for all the numbers to double 5, modelling the actions and words for the learners until they can do this for themselves.

Doubles memory game (pairs) You will need the 0–9 digit cards photocopy master (CD-ROM) to make two sets of 1 to 5 number cards.

Shuffle the cards and place them face down in a 2 by 5 grid. Learners take turns to turn over two cards. If the two cards are the same, they have to say the corresponding number sentence in order to keep the cards. For example, ‘Double four makes eight’. If the cards are not identical, they must return them face down to their original positions. The learner who collects the most cards is the winner.

Double snap (two or more players) You will need two sets of cards from the 0–9 digit cards photocopy master (CD-ROM). (Use one set of cards per player.)

Shuffle two sets of the cards. Deal all the cards out to the players, face down. Learners take it in turns to turn over their top card and place it in the middle of the table. They call out ‘Snap’ for identical cards. To keep the cards the learner must then say the corresponding number sentence, for example, ‘Double three is six’ or the cards must be returned to the middle of the table and play continues.

Dice snap (two or more players) You will need a different coloured dice for each player and some counters.

Learners each roll their dice. If both dice show the same number, the first player to say ‘double’ claims a counter. When all the counters have been taken, the learner with the most is the winner. Alternatively, the learner who first says the corresponding number sentence, ‘Double three is six,’ when the dice show three, gets the counter.

Domino hunt (groups) You will need the Dominoes photocopy master (CD-ROM).

Spread out a set of dominoes face down. Learners take turns to pick up two dominoes. They discard all the non-doubles and keep the doubles. Who has collected the most doubles by the end of the game? Use the spots to find out the totals for double 0 (blank) 1, 2, 3, 4, 5 and 6.

Core activity 2.3: Doubles

19

Ten frame

This resourse is used throughout Stage 1, see page xi.

Original Material Š Cambridge University Press, 2014

1C

3 Length

Quick reference Core activity 3.1: Measuring length (Learner’s Book p10) Learners make observations and comparisons about length. They then put different lengths into order.

Learners begin to understand that height is a length from top to bottom.

Giant footprints Vocabulary longer

shorter longer

shorter longest

shortest

How long is your footprint?

How long is the giant’s footprint?

10

Prior learning • Comparing and ordering measures (length).

• Using the language of measure (length).

• Comparing two lengths by direct comparison.

Objectives* – 1MI1 – 1MI3 – 1Pt1 – 1Pt9 –

Unit 1C Core activity 3.1 Measuring length

please note that listed objectives might only be partially covered within any given chapter but are covered fully across the book when taken as a whole

1C: Measure (Length, mass and capacity) Compare lengths and weights by direct comparison, then by using uniform non-standard units.

Use comparative language, e.g. longer, shorter, heavier, lighter.

1C: Problem solving (Using techniques and skills in solving mathematical problems) Choose appropriate strategies to carry out calculations, explaining working out.

Make a sensible estimate of a calculation, and consider whether an answer is reasonable.

*for NRICH activities mapped to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths

Vocabulary measure • size • compare • guess • estimate • about the same as • just over • just under • roughly • length • width • height • long • short • tall • longer • shorter • taller • longest • shortest • tallest

Cambridge Primary Mathematics 1 © Cambridge University Press 2014

Unit 1C

21

Core activity 3.1: Measuring length

LB: p10

Resources: Giant’s footprints made from A2 paper (make sure they are all the same width and length as each other). Materials for learners to make their own paper feet: sheets of A4 paper, pencils and scissors. Non-standard measuring devices: paper, interlocking cubes, string or ribbon. 15 cm and/ or 30 cm rulers. (Optional: Stepping stones photocopy master (CD-ROM). 1–20 tracks from the Number tracks photocopy master (chapter 4, p38) for class display.)

We are aware that activities and discussions involving bare feet are not always appropriate.

If necessary, adapt this session to ensure all footprints are made with socks/shoes kept on, or changed to hand prints.

Vocabulary

Comparing and measuring lengths

width: is the straight line distance across an object from one side to the other side.

Show learners the giant’s footprints. Make sure learners know what is meant by ‘length’ by indicating the straight line distance from heel to toe; and the ‘width’ by indicating the straight line from one side to the other at the widest part of the footprint. Discuss the length of the footprints. “What do you think could make a footprint this long?” Accept all the answers given. “Why do you think that? Does it look like your foot? Is it the same as your foot?

What is the same? What is different? Encourage use of vocabulary such as ‘longer’, ‘shorter’, ‘wider’, ‘less wide’, ‘more wide’.

Ask, “How can we find out what is the same and what is different about our footprints and the giant’s footprints?”

Draw out that we need to compare the length, width and shape of the footprints. We can do this by measuring or direct comparison.

Give pairs of learners a pencil and scissors and inform them that they are going to make their own footprints. Learners help their partner to draw round one foot and cut out their footprint. Ask learners to write their name on their own paper footprint.

Learners compare the length of their footprint with the length of the giant’s footprints.

They need to decide if they are going to use direct comparison (laying one on top of the other) or if they are going to use a non-standard measure.

Show learners the non-standard units of measure and explain how they can be used: if we were using interlocking cubes, for example, we would keep interlocking one cube to the next

22

Unit 1C

3 Length

length: is the straight line distance from one end of an object to the other end.

length

width height: is the straight line distance of an object from top to bottom. estimation: making a sensible guess based on previous knowledge.

until it matched the length of a giant’s footprint. We would then do the same with a different set of cubes for your own footprint and compare how many cubes made up each length. The learners should choose their own method and what the measure will be. Learners can draw pictures or make jottings to record their findings. Encourage them to explain their choices.

“What do you notice about the length of your footprint against the length of the giant’s footprints? What do you notice about the width of your foot and the width of the giant’s footprints? (Encourage vocabulary such as ‘smaller’, ‘shorter’, ‘less wide’, ‘longer’, ‘wider’, ‘bigger’, ‘larger’ and so on.) Find out as much as you can about your footprint and the giant’s footprints. What do we need to think about? How can you record what you find out?”

Once everyone has made and measured their footprints against the giant’s footprints, introduce the task of ordering all the footprints by length, including the giant’s footprint.

This reinforces the idea of comparing lengths relative to one another. Encourage the use of vocabulary such as ‘longest’, ‘shortest’, ‘longer’ and ‘shorter’.

Estimating lengths Make sure learners understand what is meant by ‘estimating’ and encourage them to make estimates by asking questions such as, “How many of these footprints do you think will fit into this one?” Ask them to explain their reasoning, then get them to check if they are correct by measuring. Discuss the results.

Length and height Explain that height is a type of length. It measures from the top to the bottom of an object.

Invite a learner to the front of the class and demonstrate their height. Ask learners if they think the giant who made the footprints is taller or shorter than the learner.

Ask pairs of learners to measure the height of their partner and to record it. They can use whatever equipment they like. Ask learners to line up from shortest to tallest, discussing it as a class as

they do it. (Be aware of any personal issues regarding height.) Encourage use of vocabulary such as ‘tall’, ‘tallest’, ‘taller’, ‘short’, ‘shorter’ and ‘shortest’.

End the session with further questions. “What have you found out about your footprint and the giant’s footprints? What did you do to find out? Did anyone do anything differently? What equipment did you use? How did you record what you found out? Did you use any new words today? Show or tell me what they mean.”

Look out for!

• Learners who find it difficult to estimate length with reasonable accuracy. Provide more opportunities that allow them to practise this skill.

For example, the length of a pencil, a book, their table, their stride.

• Learners who have difficulty ordering two or more items according to their length. Check why learners are making mistakes. “Do you think we need to have the ends of the items at the same place? Is that an important thing to remember?”

Demonstrate with the ends of some items at the same place and then with the ends at different starting places. “Is there a difference? Which do you think will give the best result? Why?” • Learners who have difficulty measuring lengths.

Allow more time for the skill of measuring to develop. Start with shorter items and provide different resources to measure with. For example, rigid cardboard strips with points marked might be more effective than ribbon or string that moves easily.

• Learners who have difficulty choosing appropriate strategies for measuring. Use the strategies of other learners in the class as a teaching point.

Opportunity for display • Display the learners’ footprints in order of size.

• Use the giant’s footprints to create a ‘giant walk’ around the classroom or school.

Core activity 3.1: Measuring length

23

Summary • Learners are able to compare and order lengths (and heights) using comparative language.

• They can measure lengths using direct comparison and using non-standard measures.

• They begin to understand estimating.

Notes on the Learner’s Book Giant’s footprints (p10): provides a visual reference for the Core activity. The vocabulary ‘longer’ and ‘shorter’ is explained using diagrams.

Height (p11): use the pictures as a basis for discussion. Make sure learners understand the concept of height as a length.

Check up!

• “Order the lengths of these pencils/books/ribbons from longest to shortest.”

• “Order the lengths of this range of objects.” (e.g. pencils, books, ribbons, string.)

• “Who is taller? [learner 1] or [learner 2]?”

• “Who is the shortest person in the class?”

• “Who has the biggest feet in the class?”

More activities Stepping stones (class) You will need the Stepping stones photocopy master (CD-ROM).

Give each pair of learners one giant’s footprint, one Jack’s Mother’s footprint and one Jack’s footprint from page 2 of the photocopy master (there are multiple copies of each to reduce the amount of photocopying required). Explain that each one represents a footprint but do not tell them yet who each footprint belongs to. Ask the following questions to the class, “Which footprint is the longest? Which is the shortest?” (Learners lift the bits of paper in the air in response to these questions). “One of these belongs to a giant, the other to Jack, who is 10 years old, and the other to his Mother.” Show each footprint one at time and ask, “Who does this footprint belong to? Why do you think that?” Learners should be able to recognise that the longest, widest and largest footprint will belong to the giant and the shortest, narrowest and smallest footprint will belong to Jack. Display the stepping stone path for the whole class to see (learners should also have their own copy between pairs). Explain, “The giant’s footprint is four stones long. Each time the giant takes a step, he moves forward four stones.”

Demonstrate that after two steps he has moved 8 stones along the path and that, as his footprint is 4 stones long, this is one ‘step’ for the giant. Ask, “How many steps does it take the giant to reach Jack’s house?” Give time for discussion in pairs and for the learners to move the giant’s footprint along the path, matching 4 stones of the footprint to the next four stones on the paths and then, take responses. Accept all answers and reasoning. (Answer: 9 steps) “How long is Jack’s footprint? How long is his Mother’s? Who will take more steps to reach Jack’s house, Jack or his Mother? Why?” Learners discuss their ideas in pairs and then share their answers with the class. Learners should reason that as Jack’s Mother’s footprints are longer than Jacks, she will take less steps to get back home.

All in order (groups) Ask groups of learners to arrange themselves by height starting from shortest to tallest, or tallest to shortest. (Be aware of any personal issues regarding height.)

Games Book (ISBN 9781107646407) Shoes and feet(1)–(3) (p35–36) is a series of games for pairs, threes and the whole class. They can be used to practise length comparison and vocabulary, and to encourage discussion and reasoning.

24

Unit 1C

3 Length

1A

4 Counting over ten

Quick reference Core activity 4.1: Number pairs less than ten (Learner’s Book p12) Learners practise finding number pairs for numbers less than ten.

Oh no!

Number pairs This is a number pair for

6

Vocabulary

PM_S1_U1_P10_LB_0070 PM_S1_U1_P10_LB_0070 PM_S1_U1_P10_LB_0072 PM_S1_U1_P10_LB_0072 PM_S1_U1_P10_LB_0070 PM_S1_U1_P10_LB_0072

.

Write the teen numbers in the correct order.

number pairs:

Vocabulary teen numbers: all the numbers that are made of ten and some ones.

Core activity 4.2: Ten and some more (Learner’s Book p13) Learners are introduced to all the teen numbers using two Ten frames and counters. They understand that teen numbers are ‘ten and some more’. They move on to order the numbers 1 to 20.

6 and6 and 1and51and 1 50and and650 1and is a 50 number

This is a number pair for

?

pair to 6.

PM_S1_U1_P10_LB_0074 PM_S1_U1_P10_LB_0074 PM_S1_U1_P10_LB_0076 PM_S1_U1_P10_LB_0076 PM_S1_U1_P10_LB_0074 PM_S1_U1_P10_LB_0076

.

PM_S1_U1_P16_LB_0368 PM_S1_U1_P16_LB_0368 PM_S1_U1_P16_LB_0368

Use a number track to help you.

2 and33and 3 4 and4 32 42and and4 3and is a33 number

PM_S1_U1_P16_LB_0370 PM_S1_U1_P16_LB_0370 PM_S1_U1_P16_LB_0370

pair to 7.

PM_S1_U1_P15_LB_0330 PM_S1_U1_P15_LB_0330 PM_S1_U1_P15_LB_0330

This is a number pair for

?

. This is a number pair for

?

.

PM_S1_U1_P16_LB_0372 PM_S1_U1_P16_LB_0372 PM_S1_U1_P16_LB_0372

PM_S1_U1_P16_LB_0374 PM_S1_U1_P16_LB_0374 PM_S1_U1_P16_LB_0374 PM_S1_U1_P15_LB_0340 PM_S1_U1_P15_LB_0340 PM_S1_U1_P15_LB_0340

PM_S1_U1_P16_LB_0376 PM_S1_U1_P16_LB_0376 PM_S1_U1_P16_LB_0376

12

Unit 1A Core activity 4.1 Number pairs less than ten

Unit 1A Core activity 4.2 Ten and a bit more

13

PM_S1_U1_P15_LB_0350 PM_S1_U1_P15_LB_0350 PM_S1_U1_P15_LB_0350 PM_S1_U1_P16_LB_0378 PM_S1_U1_P16_LB_0378 PM_S1_U1_P16_LB_0378

Prior learning • Count in ones to ten and beyond.

• Read and write numbers to ten and beyond.

Objectives* – 1Nn1 1Nn2 1Nn3 1Nn6 1Nn8 1Nn9

– – – – – –

1Nc1 – 1Nc2 – 1Nc8 – 1Nc9 – 1Nc11 –

please note that listed objectives might only be partially covered within any given chapter but are covered fully across the book when taken as a whole

1A: Numbers and the number system Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).

Read and write numerals from 0 to 20.

Count objects up to 20, recognising conservation of number.

Begin partitioning two-digit numbers into tens and ones and reverse.

Use more or less to compare two numbers, and give a number which lies between them.

Order numbers to at least 20, positioning on a number track; use ordinal numbers.

1A: Calculation (Mental strategies) Know all number pairs to 10 and record the related addition/subtraction facts.

Begin to know number pairs to 6, 7, 8, 9 and 10.

1A: Calculation (Addition and subtraction) Understand addition as counting on and combining two sets; record related addition sentences.

Understand subtraction as counting back and ‘take away’; record related subtraction sentences.

Add/subtract a single-digit number by counting on/back.

*for NRICH activities mapped to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths

Vocabulary addition • total • digit • number pair (or bond)

Cambridge Primary Mathematics 1 © Cambridge University Press 2014

Unit 1A

25

Core activity 4.1: Number pairs less than ten

LB: p12

Resources: Ten frame photocopy master (chapter 2, p20). Number pair frames photocopy master (p34). Resources for counting: counters, cubes or other counting objects in two different colours. (Optional: 0–9 digit cards photocopy master (CD-ROM); 1–9 dice (if not available use the 1–9 spinner photocopy master (CD-ROM). Target 5–Target 10 photocopy masters (CD-ROM).)

Begin by counting to ten and back with the learners. Remind them of the importance of ten.

Explain that we use all the numbers up to ten a great deal and it is useful to be able to spot these numbers when they are split into two parts. Tell them you will be looking at number pairs to numbers less than ten.

Show the learners a blank Ten frame and ask them to write in the numbers as shown:

1

3

5

7

9

2

4

6

8

10

Choose a focus number, such as five. Show the learners how to cut off all the numbers higher than five to create a five frame.

Alternatively, use the Number pair frames photocopy master.

Vocabulary

1

3

2

4

5

Give the learners five counters (or cubes or other counting objects) in one colour and five in another colour. Ask them to put the same coloured counter on each square of the five frame.

“How many counters do you need of the other colour to fill the five frame?” The learners will tell you that there is no more room to add other counters. Tell them that they are right, “Five and 0 makes five”. Swap one counter at one end for the other colour. “How many are there of the first colour?” (Answer: four) “How many of the second colour?” (Answer: one) With the learners, say the resulting number sentence, “4 and 1 makes 5”. Continue in this way until all the counters have been swapped for the second colour. Accept number pairs which are simply

26

Unit 1A

4 Counting over ten

Recognising number pairs to ten, and number pairs for targets below ten, is a good way to generate some simple addition and subtraction facts that will be useful for mental methods. It is also a good practical activity to reinforce addition as counting on and as combining two sets, and subtraction as counting back and taking away.

number pair (or number bond): two numbers that add together to make a particular number, e.g. 7 and 2 are a number pair for 9.

Look out for!

Learners who find the numbers on the ten frame confusing. Replace their ten frame with a blank one of the appropriate shape for the target number.

reversals, for example, 4, 1 and 1, 4, at this stage. Ask the learners to record the number pairs by colouring in the squares on a sheet of five frames, or by recording the number sentences.

For example, 5 and 0 makes 5; 5 + 0 makes 5; 5 + 0 = 5; or in some other way.

Focusing on five again, ask the learners to place one counter in each square of the five frame. Can the learners tell you how many objects they have used without counting them?

Ask each learner to take away the counter from the square labelled ‘5’. Explain that we had five and we have taken away one. “How many do we have left?” (Answer: four) You could ask the learners to record this by colouring in a five frame, or as shown here on the right.

Ask learners to return the counter to its original place, then take away two counters. “How many have we left?” (Answer: three) If you wish, record as before.

Continue until learners have taken away five. You could also take away 0.

Carry out the same activities using 6, 7, 8 and then 9 as the focus number. You might need to do these in further sessions.

Look out for!

Learners who find it easy to work out number pairs.

Challenge them to list or show the number pairs in a logical sequence.

Example: diagram to record ‘five take away one is four’.

1 5

Example: diagram to record ‘five take away two is three’.

2 5

Summary • Learners have begun to know all the number pairs (bonds) for numbers less than ten, and they can record the related addition/subtraction facts.

• They have developed strategies for finding out the number pairs they cannot recall.

Notes on the Learner’s Book Number pairs (p12): use this page for class discussion. Ask, “Which number pair is each pair of hands showing?” Encourage learners to explore number pairs for a particular number.

Learners write or draw the other number pairs for the number shown by each pair of hands.

Some number pairs cannot be easily shown using hands, for example six and two. Invite learners to come up with their own ideas.

Check up!

Use the following question stems for different target numbers up to ten.

• “If you take two away from five, how many are left?”

• “Can you tell me a number pair for five?”

• “Can you tell me all the number pairs for five?”

Core activity 4.1: Number pairs less than ten

27

More activities Two hands game (class) This activity develops instant recall of number pairs up to ten. Say a number up to ten. Learners show you that number with their fingers. They must use both hands but can make a fist for zero. Pause the game occasionally and ask the learners to sort themselves into groups of matching number pairs. “Does it matter which hand shows each part of the number pair?” Discuss which number pairs are the same. “Which number pairs cannot be made using two hands in this way?” You could keep a record of how many different number pairs there are for each number; ask learners if they can see a pattern.

Adding number pairs (individuals or pairs competing against one another) You will need the 0–9 digit cards photocopy master (CD-ROM) and a 1–9 dice.

Use the cards numbered from 1 to 9, shuffle them and place them face down in a pile. Choose a focus number from one to ten, such as seven. Turn over the top number card, the digit on this card is the first number in the pair to the target number. Learners/teams take turns to roll the dice once until one team rolls the number needed to complete the number pair using addition for the focus number. When this happen that learner/team gets a point and the card is put to the bottom of the pile and a new card is chosen. Work through the cards twice. The learner/team with the most points wins the game. (If the number on the card is larger than the focus number, learners need to realise that it is impossible to make the number pair through addition and so put this card to the bottom of the pile and select another). Extend the game to include subtraction to make the focus number. When a card is turned over that is higher than the focus number, instead of putting it to the bottom of the pile and selecting another card, learners need to roll the number which must be taken away from the card number in order to make the focus number.

Target five to ten (individuals) You will need the Target 5–Target 10 photocopy masters (CD-ROM) .

Learners circle all the number pairs that make the focus number. Number pairs could be across, down or diagonal. Each number can only be circled once.

There are several different ways to complete each target sheet, so challenge the learners to beat the best score.

Games Book (ISBN 9781107646407) Rocket launch (p6) is a game for two players. It can be used to give learners practice in adding number pairs to 12.

28

Unit 1A

4 Counting over ten

Blank page

29

Core activity 4.2: Ten and some more

LB: p13

Resources: Ten frames photocopy master (chapter 2, p20). Counters. Tens and ones arrow cards photocopy master (p36). Number tracks photocopy master (p38). 0–9 digit cards photocopy master (CD-ROM). For ordering numbers on a washing line: clothes pegs and string.

(Optional: counting objects such as coins or cubes. Tray or pot to drop coins/cubes into. Legs cards photocopy master (CD-ROM).)

Ask learners to remind you how many fingers they have and count them together. Remind them that ten is a very important number in our number system, so they already know ten very well. But numbers do not stop at ten, they go on and on. Ask the learners to count up as high as they can in order to determine how many teen numbers they know. If some learners are able to count all the way to 20, chant along as a class. If you want, you could display the 1–10 and 11–20 tracks from the Number track photocopy master. Ask learners if they know how to write the teen numbers in numerals and invite learners to do so at the front of the class. Learners might recognise some or all of the teen numbers (from extending Core activity 3.1 or from home or elsewhere) but might not really understand their value; it is important that they realise these numbers are ten and some more. The following activity will help to reinforce this.

Partitioning two-digit numbers

Vocabulary arrow cards: also known as place value cards.

1

0

teen numbers: all the numbers with one ten and some ones, e.g. 11, 12, 13, 14, 15, 16, 17, 18 and 19.

Example: using ten frames and arrow cards to show the number eleven.

Display a blank frame from the Ten frames photocopy master for the whole class to see. It should be turned so that a row of two spaces is at the top. Draw a circle/cross in each space and check that the learners can tell you that there are ten circles/crosses. Draw an arrow card for ten below the Ten frame, as per the example (1) on the right, then introduce them to an actual arrow card from the Tens and ones photocopy master.

Place a second Ten frame alongside the first. Fill the second Ten frame from the bottom up one circle/cross at a time to show learners how to make 11, 12 and then 13 all the way to 20; each time you place another circle/cross count on from ten. Remind learners that the completed frame on the left is ten, so each time you add a circle/cross to the other Ten frame you have ten and some more. Show how to make each number with arrow cards as you make it on the Ten frames. See (2) on the right.

30

Unit 1A

4 Counting over ten

7

(1)

1

(2)

0

1

1

Give each learner two Ten frames and some counters. Show them a number between 11 and 20 using the Tens and ones arrow cards photocopy master and ask them to make it on their tens frames. Occasionally reverse the activity by showing them a number on the ten frames and asking them to show the matching number with their arrow cards.

Note: It is important that you either follow up the session on 11 to 20 with a session focusing on ordering these numbers, or order the numbers on a washing line as the learners make them. This ensures that the learners begin to get the idea that each number is one more than the one before.

Prepare a set of large 1 to 20 number cards. These could be themed according to the learners’ interests such as dinosaurs, flowers, stars, football shirts and so on, or simply write large, clear numbers, with each number on a single sheet of A4 paper.

Give the large 1 to 20 number cards out to the learners. Make a washing line that is long enough to hold all the numbers and put it within reach of all the learners. Ask the learner who has the 1 card to come and peg their number on the far left of the washing line, so that all the learners can see it. Ask who has one more than one and invite them to peg their number next to 1. Keep asking who has one more until the number line is complete. Encourage the learners to count to help them name the next number, so that they understand that one more is the next counting number. You could complete one to ten before the 11 to 20 activity and the rest either as the activity progresses or immediately afterwards.

Look out for!

• Learners who clear both Ten frames to prepare for the next number. Remind everyone that the ten part is not changing, so they can keep that ready.

Each number is ten and some more.

• Learners who say ‘–ty’ instead of ‘–teen’. Show them that ‘–teen’ is just ten with an extra ‘e’, so 17 (written ‘seventeen’), is just seven and one ten.

It is important that this is corrected early on to prevent future issues.

• Learners who might be confident enough to make higher numbers. Give them the rest of the set of arrow cards and more ten frames and challenge them by giving them a particular number to make using both arrow cards and ten frames.

Return to the number line later or on another day. This time, ask a learner to remove a number which is one more than a particular number. If you have room, leave the washing line up for the learners to use regularly.

Core activity 4.2: Ten and a bit more

31

Summary Learners understand how to build numbers from 11 to 20 as ten and some more.

Check up!

Notes on the Learner’s Book Oh no! (p13): all the teen numbers have fallen off the number track. Ask the learners to draw a number track starting with ten and finishing with 20, then put the numbers in the correct order. Some learners may need to see a number track in order to draw it. If desired, use the Number tracks photocopy master and edit out the numbers between 10 and 20.

• Ask learners to show you a teen number using counters. They should arrange the counters as though on Ten frames, so that the number is clearly ten and some more.

• Ask learners to write a teen number and ask them how they know what to write.

More activities Number line again (class) You will need large 1 to 20 number cards and the washing line and pegs.

Give out the number cards but ask the learner with the 20 card to peg their number on the far right of the washing line. Ask who has one less than 20 and invite them to peg their number next to 20. Repeat until the number line is complete. Encourage the learners to count back from 20 to help them name the next number, so that they understand that one less is the previous counting number. Return to the number line later or on another day. This time, ask a learner to remove a number which is one less than a particular number.

Legs (pairs) You will need the Legs cards photocopy master (CD-ROM).

Shuffle the cards. The aim is to collect 20 legs. Players take turns to pick a card and keep it, adding up their total as they go along. Play continues until a player gets 20 legs or goes bust by collecting more than 20 legs.

Teen action (class) You will need the Tens and ones arrow cards photocopy master; use the 1–20 arrow cards.

For a quick filler activity, show the learners a teen number made from arrow cards and ask them to do a particular activity that number of times, counting their actions as they do them. Actions could include clapping; tapping their head, nose or elbow; slapping their knees; bouncing; stamping and so on. Ask one learner to repeat an action and challenge the rest of the learners to count the actions. Give several learners a turn.

32

Unit 1A

4 Counting over ten

Beyond 20 (pairs) You will need the Tens frames photocopy master and the Tens and ones photocopy master; use the 1–30 arrow cards.

Extend the activity by giving learners a third Ten frame and a set of arrow cards including the 20 arrow card from the Tens and ones arrow cards photocopy master.

Extend the numbers into the twenties. Learners work in pairs and take it in turns to make a twenty-something number using their arrow cards; then their partner has to make this number using counters on three Ten frames.

Counting together (pairs) You will need the 0–9 digit cards photocopy master (CD-ROM), the Number track photocopy master and counting items; per pair of learners.

Learners receive a ‘10’ card and a single-digit card and show the teen number using their fingers: learners take turns to show all fingers as the ten, with the other showing the ones. They then count their fingers from one to check the total and put out that number of items on the number track. Ask each pair of learners, “What would be one more? What would be one less?”

Core activity 4.2: Ten and a bit more

33

Instructions on page 26.

4 2

6

7 5 3 1

8 4 2

6

7 3 1

5

4 2

6

8

9 7 3 1

5

10 8 4 2

6

3 1

5

7

9

Number pair frames

Original Material Š Cambridge University Press, 2014

4

3

4

2

1

2

2

5 3 1 1

6 4 2 2

1

3

1

3

5

Number pair frames

Instructions on page 26.

Original Material Š Cambridge University Press, 2014

Instructions on pages 30–31.

1 1 2 3 4

Original Material Š Cambridge University Press, 2014

0 0 0 0 0 0

Tens and ones arrow cards

4 3 2 1

0 0 0 0 0 Original Material Š Cambridge University Press, 2014

9 8 7 6 5

5 6 7 8 9 Instructions on pages 30–31.

12 22 32 42 52 62 72 82 92

11 21 31 41 51 61 71 81 91

93

83

73

63

53

43

33

23

13

3

This resource is used throughout Stage 1.

2

1

94

84

74

64

54

44

34

24

14

4

95

85

75

65

55

45

35

25

15

5

96

86

76

66

56

46

36

26

16

6

98

88

78

68

58

48

38

28

18

8

99

89

79

69

59

49

39

29

19

9

100

90

80

70

60

50

40

30

20

10

Original Material Š Cambridge University Press, 2014

97

87

77

67

57

47

37

27

17

7

Number tracks

1A

5 Estimating

Quick reference Core activity 5.1: Estimating (Learner’s Book p14) Pairs of learners estimate how many and then check their estimate by counting.

They discuss the accuracy of their estimate.

Estimate and count

Twice as many?

How many?

Vocabulary count:

estimate:

Vocabulary

twice as many

How many? twice as many

Core activity 5. 2: More estimating (Learner’s Book p15) Learners extend their counting range and refine their estimation skills.

Is this twice as many?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10 twice as many

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 14

Prior learning • Count in ones beyond ten.

• Read and write numbers to ten and beyond.

Objectives* – 1Nn1 1Nn2 1Nn3 1Nn11 1Nn8

– – – – –

1Pt2 – 1Pt4 –

How do you know?

Unit 1A Core activity 5.1 Estimating

Unit 1A Core activity 5.2 More estimating

15

please note that listed objectives might only be partially covered within any given chapter but are covered fully across the book when taken as a whole

1A: Numbers and the number system Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).

Read and write numerals from 0 to 20.

Count objects up to 20, recognising conservation of number.

Use more or less to compare two numbers, and give a number which lies between them.

Give a sensible estimate of some objects that can be checked by counting, e.g. to 30.

1A: Problem solving Explore number problems and puzzles.

Decide to add or subtract to solve a simple word problem (oral), and represent it with objects.

*for NRICH activities mapped to the Cambridge Primary objectives, please visit www.cie.org.uk/cambridgeprimarymaths

Vocabulary how many? • count • estimate • total • twice • more • less

Cambridge Primary Mathematics 1 © Cambridge University Press 2014

Unit 1A

39

Core activity 5.1: Estimating

LB: p14

Resources: Number tracks photocopy master (chapter 4, p38); large version for class display. Resources for counting, such as bead strings (with at least 30 beads); interlinking cubes; coins or counters. Resources for estimating: a transparent (see-through) plastic container with lid, such as a jar, containing around 18 of an object. Empty jars or yoghurt pots of a similar size to the sealed jar: one identical jar to the sealed one would be useful.

Sticky notes or paper and tape. (Optional: a collection of between 11 and 30 items contained in a bag/tray/pot for each pair of learners.)

Counting to 30 Reinforce the value of numbers above ten by first counting together to ten. Use a large copy of the 1–10 number track from the Number track photocopy master for class display; then count without it displayed. If you have bead strings, show the learners how to slide one bead along each time they say a number. Alternatively, you could drop one cube or coin on to a tray as you count together. Show a large copy of the 11–20 number track and use it to extend the 1 to 10 track. Count together, using the tracks for support and continuing to move beads or drop coins/cubes as you count to help give a sense of the size of each number.

Repeat the counting, removing the 1 to 10 track first, then the 11 to 20 track. Extend to include 21 to 30 if the learners are confident with the lower numbers.

How many in the jar?

Show the learners the transparent sealed container and explain that you would like to know how many items there are inside it but the lid is stuck. “How many [objects of choice] are in the jar? What is your estimate?” If necessary explain the word ‘estimate’; learners might remember this from the giant footprint activity, if not, remind them that it is a sensible guess using known information. For example, if they know what ten of the object looks like they can use that as a guide to help them guess how many more/less than ten there might be of the object.

If high estimates are offered, show the learners ten and 100 of the object that is contained in the jar and ask, “Which is most like what is in the jar?” Give learners a chance to revise their estimates, if necessary, and record the estimates on the board.

40

Unit 1A

5 Estimating

Vocabulary estimate: a sensible guess at how many (or how much) using any known information. total: how many altogether; i.e. how much of something there is. twice: two times or two lots of an amount. more: when there is a larger number/amount of something. less: when there is a smaller number/amount of something.

Look out for!

Learners who do not yet have a concept of how much ten is and are unable to give a reasonable estimate. These learners are not ready to give an estimate, but will still benefit from the counting and comparing parts of this activity.

Explain that it would be useful to see what the estimates look like.

Learners work in pairs to agree an estimate and then count out that many of the object. Explain to them what is meant by the term ‘total’, and that they must check their total by putting one object on each number on the number track in the Learner’s Book (p12). The objects should then be put in a jar or yoghurt pot similar in size to the sealed jar. Each pair of learners needs to decide if what they have counted ‘looks right’. If they are not happy they can change the amount, adding one more or taking one away until they are happy. Once they are happy, they write the total on a sticky note or similar. The learners then attach the label to the jar or yoghurt pot.

Gather the learners together and ask if anyone would like to change their estimate on the board now they have done some counting. When everyone is happy, discuss the estimates. How many learners think there are 11? 12? etc. Ask questions such as, “What makes you think that? Does your number of objects look the same as mine if we put yours in the similar jar? Does it look as though there are too many or not enough?”

Now undo the stuck jar (to be in the theme of the initial problem, pretend to do so with a great deal of effort, or by asking another adult to try). Carefully count the items together, crossing off each number on a giant number track in turn. Agree the total.

Discuss which estimates were very close or even exactly right. Congratulate the learners on their counting skills. Ask questions such as, “Is there more/less in the jar than you estimated?” And encourage use of vocabulary such as ‘more’, ‘less’, ‘about the same’, ‘twice as many’.

Look out for!

• Learners who leave gaps when placing items on the number track. Explain that they must begin by placing one of the items to be counted on number 1 and then use the next square until they have run out of items to count, otherwise the total will not be correct.

• Learners who do not recognise that the last number on the number track with an item on it is the total number of items. Continue to emphasise that the last number spoken is the total; there is no need to recount.

• Learners who place an item on their estimated total first, then backfill to get the correct amount. Working in this way demonstrates a clear recognition that the last number used is the total. These learners do not need to use the number tracks and could count their estimate straight into their jar or pot.

Opportunity for display Display the labelled pots on a table with some number tracks. Add a sign inviting learners and parents to check the counts.

Take opportunities to ask for estimates during other classroom activities.

Summary Learners can estimate how many and check their estimate by counting.

Notes on the Learner’s Book Estimate and count (p14): provides a number track to help the learners count items during the Core activity. Learners can also use the number track to find out ‘how many’ during other counting activities.

Check up!

• Ask learners to count out a number of items, for example, 17, with or without using the number track.

• Create piles/jars/containers of known amounts of an object and ask learners to estimate how many there are, and then justify their reasoning. Ask learners to count the items to check how close their estimates are.

Core activity 5.1: Estimating

41